FIG. 1 illustrates a motor vehicle 3, which contains a sun roof (not shown) within dashed box 6. FIG. 2 is a view, looking downward, onto the sun roof 9. If, in FIG. 3, an obstruction 10 is present which blocks closure of the glass window 12, motion of the window 12 should generally be stopped, or reversed.
Various stratagems exist in the prior art to achieve this stoppage. Clutches are used, which stop motion of the window 12 when the window 12 strikes the obstruction 10. The obstruction 10 causes an opposing force which overrides the clutch.
Also, sensors are used, which sense the presence of objects in the path of the window 12. Other sensors are used which sense electrical parameters of the motor driving the window. For example, current drawn by the motor can increase when load on the motor increases. Obstruction 10 increases the load, when the window 12 meets the obstruction 10. A system can detect the resulting increase in current, and shut down, or reverse, the motor in response.
In general, assume a sequence of events, and that a certain parameter has a value which can change upon each event. For example, the events may be the passage of units of time, such as one second each, and the parameter may be a velocity or a temperature, which can change every second.
As another example, the events may be individual revolutions of a shaft. The parameter may be speed of the shaft, or the period of revolution of the shaft, which can change every revolution, and each revolution represents one of the events.
Thus, a sequence of parameters P1, P2, P3, etc. has been described, and each parameter is measured every time the event occurs.
Consider the differential between two succeeding parameters, such as (P2−P1). That differential can be normalized, by dividing by a value assigned to the event. For example, if the parameters are velocity, and the event is the passage of one second, the normalization results in the quantity (V2−V1)/(one second). This quantity is the rate of change of speed, or acceleration.
As another example, if the parameters are period T of revolution of a shaft, and the event is one revolution of the shaft, the normalization results in the quantity (T2−T1)/(one revolution). This quantity is the rate of change of period per revolution.
In general, if one begins with a starting value of the parameter, one can compute a subsequent value of the parameter using the differentials and the events, in the following manner:Pf=Pi+dP1(E)+dP2(E)+dP3(E)+ . . . +dPN(E),wherein    Pf is the final value of the parameter,    Pi is the initial value,    dP is the differential between two successive parameters, and    E is the event, in appropriate units.    This type of computation will be elaborated, initially in the context of velocity and acceleration.
A basic velocity equation found in engineering is the following:Vo=Vi+Atwherein    Vo is final velocity,    Vi is initial velocity,A is acceleration, andt is time.
If acceleration is measured at one-second intervals, then a variation of this equation is the following:Vo=Vi+A1+A2+A3+ . . . +ANwherein    Vo is final velocity,    Vi is initial velocity,    A1 is acceleration for a first one-second period,    A2 is acceleration for a second one-second period,    A3 is acceleration for a third one-second period, and    AN is acceleration for the Nth one-second period.    The Inventor points out that time, t, is not expressly present, because each acceleration occurs over a one-second interval, so that t is unity, and t is not expressed.
FIG. 11 provides an example of the computation. The plot indicates velocity of an object, as a function of time. A1 is acceleration for the one-second period prior to time of 1 second. A2 is acceleration for the one-second period prior to time of 2 seconds, and so on.
The expression for determining velocity at the time of 4 seconds isVf=Vo+A1(t)+A2(t)+A3(t)+A4(t).    Since V0 is zero, and t equals unity, the expression reduces toVf=A1+A2+A3+A4,consistent with that given at the bottom of the Figure.
FIG. 11 is framed in terms of a velocity of feet per second. However, the principles just described also apply if velocity is expressed in terms of radians per second, or revolutions per second, as occurs in rotational motion.
FIG. 11 was also framed in terms of an acceleration expressed as the change in speed per second. However, acceleration can also be expressed as a change in speed per revolution. The principles described above also apply in this case, as FIG. 12 indicates. In FIG. 12, the speed is expressed as surface speed of a rotating shaft. But the same computation as described above can be undertaken, as indicated by the equations at the bottom of the Figure.
In the general case, the principles described above can be applied to any time-changing variable. The general framework is to first measure the change in the variable over a standardized interval, or event, such as one second or one revolution. That change is analogous to the acceleration discussed above. Then the following expression is computed:Vf=Vi+A1(t)+A2(t)+A3(t)+A4(t)+ . . . +AN(t).
If the variable t (one second or one revolution, for example) has a value of unity, the expression reduces toVf=Vi+A1+A2+A3+A4+ . . . +AN.
That is, the final value of the variable V equals the initial value Vi plus the sum of the “accelerations” occurring during each second or each revolution.
FIG. 13 provides an example of the computation. In the Figure, the variable is the period required for the moving body in FIG. 11 to travel one foot. That is, at time 1 second in FIG. 11, the body is moving at 10 feet/sec. That corresponds to a period of 0.1 second per foot, or 6/60seconds in FIG. 13.
At time 2 seconds in FIG. 11, the body is moving at 30 feet/sec. That corresponds to a period of 2/60 second per foot, as indicated in FIG. 13.
For simplicity, assume that the body was moving at 10 feet per second at time zero. This assumption removes the singularity which occurs at the start-up from zero velocity. That is, at zero velocity, a period of infinity exists, which is a singularity. This assumption removes the problems of computation created by the singularity.
In FIG. 13, the “accelerations” will be termed period-accelerations, and given the symbol PA. That is, the acceleration is the change in period, per unit time. PA2 equals the change-in-period during the period ending at 2 seconds, and equals P2−P1, as indicated. PA3 equals the change-in-period during the period ending at 3 seconds, and equals P3−P2, as indicated. PA4 equals the change-in-period during the period ending at 4 seconds, and equals P4−P3, as indicated.
Note that the PA's represent both (1) the differential between subsequent periods and (2) if divided by the quantity one second, which does not change PA, the rate of change in period per second.
Thus, the value of the period at time 4 seconds is computed from the following expression:P4=P1+PA2(t)+PA3(t)+PA4(t).Since t equals unity, the expression reduces toP4=P1+PA2+PA3+PA4,which is consistent with the last expression in FIG. 10.
FIG. 14 illustrates how subsequent periods can be computed, using the period at 4 seconds as a baseline. It should be observed that, in expressions such as “P5=1/60+1/60,” the first “1/60” represents the value of the initial period, in which the units are seconds. The second “1/60” represents the “deceleration” (ie, negative acceleration) multiplied by a unit of time, with that unit being unity. The units of “deceleration” in this case are seconds/foot per second, or seconds/(foot-second), which equals 1/foot. When that is multiplied by t, the units become seconds/foot, consistent with the units of the period.
In FIGS. 13 and 14, the “deceleration” was measured over intervals of one second. As explained above, the “deceleration” can be measured over other intervals, or events, such as intervals of one revolution. FIG. 15 illustrates a plot of a period plotted against revolutions. The principles described above apply to FIG. 15, but the computations are not shown because they are the same type as in FIGS. 14 and 15.
Therefore, the general procedure is the following. Assume a parameter, or variable, V which changes over time, upon the occurrence of a sequence of events. V is measured at each event. Thus, a string of variables V(1), V(2), V(3), V(4), etc is obtained.
Next, the change in V between successive intervals is computed. This was called “deceleration” earlier, but can also be referred to as a differential, in the calculus sense. In the current example, the differentials areD2=V(2)−V(1)D3=V(3)−V(2)D4−V(4)−V(3)                and so on.        
Each differential can be divided by the quantity (one event), which will not change the value of the differential, but will convert the differential into a rate-of-change of the parameter, per event. For example, if the parameter is velocity, then one of the differentials may be V2−V1. If that is divided by one second, the quantity becomes (V2−V1)/(one second), which is the rate of change of velocity during that second.
The value of V at any time can be computed by the following expression:Vf=Vi+D2(t)+D3(t)+D4(t)+ . . . +DN(t).    Since t equals represents one event, such as one second, this expression reduces toVf=Vi+D2+D3+D4+ . . . +DN.
That is, the final value of the variable equals (1) the initial value of the variable plus (2) the sum of the differentials occurring since the initial value. Each differential is implicitly multiplied by a factor of one event, which has the units of seconds, revolutions, or whatever event is being used, and over which the differential was taken.
This type of computation will be explained in the context of the present invention.